As far as I know, the gubbins for deciding whether somewhere was a city or not was retinkered with and it was decided that the Fair City was a city and isn't a city anymore. The "Fair City" signs came down and Perth became "The Heart of Scotland"? Only 3 UK cities have ever been declassified. To me it has always been a city and I still see it as one; I would assume that long term (or born and bred) Perth folk feel that but stronger than I do.
To be honest I don't know exactly why, hopefully some of our illustrious Perth dwelling CBFers can explain.